Miami - Adding Ray Allen to your bench would be a significant upgrade for any team.

But when the Miami Heat does it, watch out.

The Milwaukee Bucks discovered that in Game 1 of their Eastern Conference playoff series Sunday night when the former Bucks guard scored 20 points to help the Heat grab a 110-87 victory.

And Allen wasn't even hitting his patented three-pointer, going just 2 for 8 from beyond the arc. But he got to the line and made 6 of 6 foul shots while adding five rebounds and three assists in 29 minutes.

"It's important whoever is coming off the bench to be aggressive," Allen said after the Heat's practice Monday. "We see what the starting five is doing and we don't want to come off the bench and turn into an all-perimeter team.

"Especially when their shot blocker ( Larry Sanders) was in foul trouble, we have to attack them in the paint."

Allen challenged LeBron James and Mario Chalmers to a three-point shooting contest after practice, and James won while needling his teammates all the way through.

But it's Allen who is on the verge of becoming the all-time leader in threes in the postseason, just five away from Reggie Miller's record of 320. Allen already is the all-time leader in regular-season threes after topping Miller's record in February 2011, as a member of the Boston Celtics.

"You add another guy who is diligent and dedicated to his craft," Heat coach Erik Spoelstra said of the 37-year-old Allen, signed as a free agent in the off-season.

"To see another guy who has a routine that no matter what, rain, shine, injury, flu, he'll always be there, it's a great example.

"I call him 'Everyday Ray,' for that reason. It's every single day. It's not every other day. It's not on days I feel like it; it's not only on days where I have my health.

"Every single day on the road he will be there on the early bus. We had to create that early bus; we didn't have that before Ray.

"That shot does not happen by accident."

The Heat also got a huge lift from Chris "Birdman" Andersen, who had four dunks, seven rebounds and 10 points in Game 1.

"He has an impact every single time he plays," Spoelstra said. "You love to see the fans show gratitude and reward him for that effort.

"The overwhelming majority of Chris' plays do not show up in a box score. We're grateful to have him. I think he's grateful to be part of this situation, and right now it fits."

More scorers needed: The Bucks struggled to find any kind of scoring help for Brandon Jennings and Monta Ellis in Game 1.

They combined for 48 points, but the rest of the team had just 39.

Two obvious candidates are sharpshooters Mike Dunleavy and J.J. Redick. Dunleavy had five points in 17 minutes in the series opener and Redick was just 1 for 6 and had six points in 16 minutes.

"It's all dependent on how much they want to play us, really," Dunleavy said. "They know what we can give. We'll be ready.

"At some point, we have a rotation and you either stick with it or change it. We'll see what happens. I feel like when our number is called we'll be ready."